If Angela runs up 5 steps of the escalator, then it takes her 40 seconds to reach the top of the escalator. If she runs up 14 steps of the escalator, then it takes her only 26 seconds to reach the top.
If Angela runs up 5 steps of an escalator, it takes her 40 seconds to reach the top of the escalator. If she runs up 14 steps of the escalator, then it takes her only 26 seconds to reach the top.
How many seconds would it take Angela to reach the top if she did not run up any steps of the escalator at all?
If I had ten and one half of beef and five an one half of pork and I used thirteen an two thirds what's left
To solve this problem, we can set up a system of equations. Let's call the speed of the escalator "e" (in steps per second) and the speed at which Angela runs "r" (in steps per second).
From the given information, we know that when Angela runs up 5 steps of the escalator, the combined speed of Angela and the escalator is equal to the distance of the escalator divided by the time it takes:
(e + r) = 5 / 40 -- Equation 1
Similarly, when Angela runs up 14 steps of the escalator, we have:
(e + r) = 14 / 26 -- Equation 2
Now, we can solve this system of equations to find the values of "e" and "r".
Multiplying both sides of Equation 1 by 40 and Equation 2 by 26, we get:
40(e + r) = 5 -- Equation 3
26(e + r) = 14 -- Equation 4
Expanding the equations, we now have:
40e + 40r = 5 -- Equation 3
26e + 26r = 14 -- Equation 4
To solve this system of equations, we can use the method of elimination. Multiplying Equation 4 by 2, we get:
52e + 52r = 28 -- Equation 5
Subtracting Equation 3 from Equation 5 gives us:
52e + 52r - 40e - 40r = 28 - 5
12e + 12r = 23
Dividing both sides of the equation by 12, we get:
e + r = 23 / 12
So the combined speed of the escalator and Angela's running is 23/12 steps per second.
Now, let's substitute this value back into either Equation 3 or 4. Let's use Equation 3:
40e + 40r = 5
Substituting e + r = 23/12, we get:
40(23/12) = 5
920/12 = 5
920 = 60
Now, we can solve for "r" by subtracting e from both sides of e + r = 23/12:
r = 23/12 - e
Substituting the value of e we obtained earlier:
r = 23/12 - 920/12
r = -897/12
So Angela's running speed is -897/12 steps per second. However, this negative value doesn't make sense in this context, so there might be a mistake in the problem or the calculations.
Please double-check the problem and make sure all values are entered correctly.